Model reduction for the collective dynamics of globally coupled oscillators: From finite networks to the thermodynamic limit.
Model reduction for the collective dynamics of globally coupled oscillators: From finite networks to the thermodynamic limit.
复制标题
全局耦合振荡器集体动力学的模型简化：从有限网络到热力学极限。
作者：
Lachlan D. Smith;G. Gottwald
模型降阶技术已被广泛应用于研究全局耦合振子的集体行为。然而，大多数方法都假设有无限多的振荡器。在这里，我们提出了一种新的基于集体坐标方法的ANSAZ方法，它高精度地再现了有限网络的Kuramoto模型的集体动力学，在无限多振子的热力学极限中产生了与以前方法相同的分叉结构，并另外捕捉了热力学极限中序参数的动力学，包括由鞍结级联分叉引起的临界减速。
Model reduction techniques have been widely used to study the collective behavior of globally coupled oscillators. However, most approaches assume that there are infinitely many oscillators. Here, we propose a new ansatz, based on the collective coordinate approach, that reproduces the collective dynamics of the Kuramoto model for finite networks to high accuracy, yields the same bifurcation structure in the thermodynamic limit of infinitely many oscillators as previous approaches, and additionally captures the dynamics of the order parameter in the thermodynamic limit, including critical slowing down that results from a cascade of saddle-node bifurcations.